In phase modulation, the instantaneous amplitude of the baseband signal modifies the phase of the carrier signal keeping its amplitude and frequency constant. The phase of a carrier signal is modulated to follow the changing signal level (amplitude) of the message signal. The peak amplitude and the frequency of the carrier signal are maintained constant, but as the amplitude of the message signal changes, the phase of the carrier changes correspondingly.
In general form, an analog modulation process of a sinusoidal carrier wave may be described by the following equation:[1]
.
A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency, and the instantaneous phase deviation . This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In amplitude modulation, the angle term is held constant, while in angle modulation the term A(t) is constant and the second term of the equation has a functional relationship to the modulating message signal.
The functional form of the cosine term, which contains the expression of the instantaneous phase as its argument, provides the distinction of the two types of angle modulation, frequency modulation (FM) and phase modulation (PM).[2]
The modulating wave (blue) is modulating the carrier wave (red), resulting the PM signal (green).
g(t) = π/2×sin[ 2×2π t + π/2×sin( 3×2π t ) ]
In FM the message signal causes a functional variation of the carrier frequency. These variations are controlled by both the frequency and the amplitude of the modulating wave.
In phase modulation, the instantaneous phase deviation (phase angle) of the carrier is controlled by the modulating waveform, such that the principal frequency remains constant.
In principle, the modulating signal in both frequency and phase modulation may either be analog in nature, or it may be digital.
The mathematics of the spectral behaviour reveals that there are two regions of particular interest:
As with other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase of the carrier signal:
where is the peak phase deviation. Compare to the modulation index for frequency modulation.
^Klie, Robert H.; Bell Telephone Laboratories; AT&T (1977). Principles. Telecommunication Transmission Engineering. Vol. 1 (2nd ed.). Bell Center for Technical Education. ISBN0-932764-13-4. OCLC894686224.
^Haykin, Simon (2001). Communication Systems. Wiley. p. 107. ISBN0-471-17869-1.
.
,
and 
is the modulation index defined below. This is also known as Carson's Rule for PM.
